Basic Analysis > Distributions > Details for the Legacy Distribution Fitters > Statistical Details for Fit Distribution Options (Legacy)
Publication date: 11/10/2021

## Statistical Details for Fit Distribution Options (Legacy)

This section describes Goodness of Fit tests for fitting distributions and statistical details for specification limits pertaining to fitted distributions.

Note: Some features of distribution fitting have been updated in JMP 15. This section contains details of the older features from previous JMP releases that have been retained for compatibility purposes. These features are available by selecting Continuous Fit > Enable Legacy Fitters in the red triangle menu for a variable.

### Goodness of Fit

Table 3.2 Descriptions of JMP Goodness of Fit Tests

Distribution

Parameters

Goodness of Fit Test

Normal1

μ and σ are unknown

Shapiro-Wilk (for n 2000) Kolmogorov-Smirnov-Lillefors (for n > 2000)

μ and σ are both known

Kolmogorov-Smirnov-Lillefors

either μ or σ is known

(none)

LogNormal

μ and σ are known or unknown

Kolmogorov's D

Weibull

α and β known or unknown

Cramér-von Mises W2

Weibull with threshold

α, β and θ known or unknown

Cramér-von Mises W2

Extreme Value

α and β known or unknown

Cramér-von Mises W2

Exponential

σ is known or unknown

Kolmogorov's D

Gamma

α and σ are known

Cramér-von Mises W2

either α or σ is unknown

(none)

Beta

α and β are known

Kolmogorov's D

either α or β is unknown

(none)

Binomial

ρ is known or unknown and n is known

Kolmogorov's D (for n 30) Pearson χ2 (for n > 30)

Beta Binomial

ρ and δ known or unknown

Kolmogorov's D (for n 30) Pearson χ2 (for n > 30)

Poisson

λ known or unknown

Kolmogorov's D (for n 30) Pearson χ2 (for n > 30)

Gamma Poisson

λ or σ known or unknown

Kolmogorov's D (for n 30) Pearson χ2 (for n > 30)

1 For the three Johnson distributions and the Glog distribution, the data are transformed to Normal, then the appropriate test of normality is performed.

### Set Spec Limits for K Sigma

Type a K value and select one-sided or two-sided for your process capability analysis. Tail probabilities corresponding to K standard deviations are computed from the Normal distribution. The probabilities are converted to quantiles for the specific distribution that you have fitted. The resulting quantiles are used for specification limits in the process capability analysis. This option is similar to the Quantiles option, but you provide K instead of probabilities. K corresponds to the number of standard deviations that the specification limits are away from the mean.

For example, for a Normal distribution, where K = 3, the 3 standard deviations below and above the mean correspond to the 0.00135th quantile and 0.99865th quantile, respectively. The lower specification limit is set at the 0.00135th quantile, and the upper specification limit is set at the 0.99865th quantile of the fitted distribution. A process capability analysis is returned based on those specification limits.